Solving Pppp-Complete Problems Using Knowledge Compilation

Knowledge compilation has been successfully used to solve beyond NP problems, including some PP-complete and NPPP-complete problems for Bayesian networks. In this work we show how knowledge compilation can be used to solve problems in the more intractable complexity class PPPP. This class contains NPPP and includes interesting AI problems, such as non-myopic value of information. We show how to solve the prototypical PPPP-complete problem MAJ-MAJSAT in linear-time once the problem instance is compiled into a special class of Sentential Decision Diagrams. To show the practical value of our approach, we adapt it to answer the Same-Decision Probability (SDP) query, which was recently introduced for Bayesian networks. The SDP problem is also PPPP-complete. It is a value-of-information query that quantifies the robustness of threshold-based decisions and comes with a corresponding algorithm that was also recently proposed. We present favorable experimental results, comparing our new algorithm based on knowledge compilation with the state-of-the-art algorithm for computing the SDP.